5(r-5)-4(r-1)=2(r+5)

Solution for 5(r-5)-4(r-1)=2(r+5) equation:

Simplifying
5(r + -5) + -4(r + -1) = 2(r + 5)

Reorder the terms:
5(-5 + r) + -4(r + -1) = 2(r + 5)
(-5 * 5 + r * 5) + -4(r + -1) = 2(r + 5)
(-25 + 5r) + -4(r + -1) = 2(r + 5)

Reorder the terms:
-25 + 5r + -4(-1 + r) = 2(r + 5)
-25 + 5r + (-1 * -4 + r * -4) = 2(r + 5)
-25 + 5r + (4 + -4r) = 2(r + 5)

Reorder the terms:
-25 + 4 + 5r + -4r = 2(r + 5)

Combine like terms: -25 + 4 = -21
-21 + 5r + -4r = 2(r + 5)

Combine like terms: 5r + -4r = 1r
-21 + 1r = 2(r + 5)

Reorder the terms:
-21 + 1r = 2(5 + r)
-21 + 1r = (5 * 2 + r * 2)
-21 + 1r = (10 + 2r)

Solving
-21 + 1r = 10 + 2r

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-2r' to each side of the equation.
-21 + 1r + -2r = 10 + 2r + -2r

Combine like terms: 1r + -2r = -1r
-21 + -1r = 10 + 2r + -2r

Combine like terms: 2r + -2r = 0
-21 + -1r = 10 + 0
-21 + -1r = 10

Add '21' to each side of the equation.
-21 + 21 + -1r = 10 + 21

Combine like terms: -21 + 21 = 0
0 + -1r = 10 + 21
-1r = 10 + 21

Combine like terms: 10 + 21 = 31
-1r = 31

Divide each side by '-1'.
r = -31

Simplifying
r = -31